Question

determine if the triangles are similar. if so, state the postulate or theorem and write the similarity statement.

Explanation:

Step1: Identify vertical angles

$\angle AEB$ and $\angle DEC$ are vertical - angles, so $\angle AEB=\angle DEC$.

Step2: Check for congruent sides

We are given that $\overline{AE}\cong\overline{DE}$ and $\overline{BE}\cong\overline{CE}$.

Step3: Apply the Side - Angle - Side (SAS) similarity theorem

Since $\frac{AE}{DE} = 1$, $\frac{BE}{CE}=1$ and $\angle AEB=\angle DEC$, by the SAS similarity theorem, $\triangle AEB\sim\triangle DEC$.

Answer:

The triangles $\triangle AEB$ and $\triangle DEC$ are similar by the Side - Angle - Side (SAS) similarity theorem.